Timeline for What is the expected value for this
Current License: CC BY-SA 3.0
12 events
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| Jan 21, 2013 at 7:06 | comment | added | user0o | Dear Gerald, yes, the random points are independent, and for a given point, the horizontal and vertical coordinates are also independent. Thank you for your questions that make this clear. | |
| Jan 19, 2013 at 13:35 | comment | added | Gerald Edgar | Probability distribution not clear: Are the points independent? For a given point, are the horizontal and vertical coordinates independent? | |
| Jan 19, 2013 at 13:26 | answer | added | Omer | timeline score: 3 | |
| Jan 17, 2013 at 22:02 | comment | added | Gerry Myerson | Also posted to math.stackexchange.com/questions/280648/… originally with $16$ points, then edited to $4$ points. | |
| Jan 17, 2013 at 20:58 | history | edited | user0o |
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| Jan 17, 2013 at 20:55 | comment | added | Sam Hopkins | I haven't really thought about it, but you should be able to recast the problem in graph-theoretic terms and then use some probabilistic tools, similar to the proof of Ramsey number bounds. | |
| Jan 17, 2013 at 20:49 | comment | added | user0o | @Sam: do you know about the probability that the extremal configurations in generalized happy ending problem occur for $8$ points or less? | |
| Jan 17, 2013 at 20:44 | history | edited | user0o | CC BY-SA 3.0 |
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| Jan 17, 2013 at 20:44 | comment | added | user0o | @Berlusconi: it does not need to 16. An answer for any number less than or equal to $8$ would be highly appreciated. It may not be trivial to solve for a large number, but one can probably have some probability estimates on the angles, which largely determine the convexity. | |
| Jan 17, 2013 at 20:22 | comment | added | Sam Hopkins | Related: en.wikipedia.org/wiki/Happy_ending_problem | |
| Jan 17, 2013 at 20:14 | comment | added | user0o | By the way, "size" only means cardinality here. | |
| Jan 17, 2013 at 20:09 | history | asked | user0o | CC BY-SA 3.0 |